Question

(sin a+cos a)^2+(sin-cos a)^2=

Answer 1

$(sin \alpha +cos \alpha ) ^{2} +(sin \alpha -cos \alpha ) ^{2} =\\ =sin^{2} \alpha +2sin \alpha cos \alpha+cos ^{2} \alpha +sin^{2} \alpha -2sin \alpha cos \alpha+cos ^{2} \alpha = \\ =2sin^{2} \alpha +2cos ^{2} \alpha= \\ =2(sin^{2} \alpha+cos ^{2} \alpha)=2*1=2$